Question

What is the derivative of z=3x*logx+5x^6 e^x with respect to x?

(a) 3+30x^5 e^x

(b) 3+5x^6 e^x+30x^5 e^x

(c) 3+5x^6 e^x

(d) 3+3logx+5x^6 e^x+30x^5 e^x

I got this question in examination.

I need to ask this question from Total Derivative in portion Partial Differentiation of Engineering Mathematics

Answer 1

Correct option is (d) 3+3logx+5x^6 e^x+30x^5 e^x

The explanation: Given: z=3x*logx+5x^6 e^x

\(\frac{dz}{dx}=3x(\frac{1}{x})\)+3logx+5x^6 e^x+30x^5 e^x

\(\frac{dz}{dx}\)=3+3logx+5x^6 e^x+30x^5 e^x